Please help me! Urgent, thanks!

The lowest common multiple of 60, 156 and n is 10920. Find the smallest possible value of n.

60 = 2² x 3 x 5
156 = 2² x 3 x 13
10920 = 2³ x 3 x 5 x 7 x 13

so hmmm we look at hmm x³ + x² - 8x - 6 so how do squeak out a factor out of it, well, using the rational root test and using our p/q checking for factors, we find that likely factors can be ± 6/1 and ±(3, 2, 1) / 1, anyhow so we check some of those and hopefully without boring you to death we find that -3 works, we can always use the remainder theorem to check if that's true, by simply plugin in f(-3) and if it's indeed a factor, that'd give us 0, well, f(-3) = -27 + 9 +24 +6 = 0, holly smokes!! is a factor.

well, all that jazz means that -3 is a factor, namely the factor is really x = -3 or x + 3 = 0 so the factor is (x+3) and for our synthetic division we'll use the -3 version, Check the picture below.

so we end up with the factors of (x+3)(x²-2x-2), now for the 2nd factor what we can do to break it up is use the quadratic formula

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-2}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}[/tex]

[tex]x= \cfrac{ - (-2) \pm \sqrt { (-2)^2 -4(1)(-2)}}{2(1)} \implies x = \cfrac{ 2 \pm \sqrt { 4 +8}}{ 2 } \\\\\\ x= \cfrac{ 2 \pm \sqrt { 12 }}{ 2 }\implies x=\cfrac{2\pm\sqrt{2^2\cdot 3}}{2}\implies x=\cfrac{2\pm 2\sqrt{3}}{2}\implies x=1\pm\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} (x+3)(x-1+\sqrt{3})(x-1-\sqrt{3}) \end{array}}~\hfill[/tex]

now, just to clarify, all those are real roots, and the last two come from simply setting x = 1 ± √3 to 0 to get the factors.

Answer:

X=9

Step-by-step explanation:

A circle adds up to 360°

63+89+73= 225

360-225= 135

Since 15x

135÷15=9

x=9

Answer:

176

Step-by-step explanation:

2+62+77= 141

62/141

400 x 62/141 = 175.8

=176

The steps for measuring the angle b is shown below, <b= 41.

If a triangle side is created, the outside angle that results is equal to the sum  of the two opposite internal angles.

If an equivalent angle is measured at each triangle vertex, the exterior angles always add up to 360 degrees.

Given:

exterior angle = 113

and, opposite interior angle =72

Using Exterior angle property we have

72 + b = 113

Subtract 72 from both side

72 + b -72 = 113 -72

b = 113- 72

b = 41

Hence, the measure of b is 41 degree.

Learn more about Exterior Angle Property here:

https://brainly.com/question/19562895

#SPJ1

Answer:

a₄ = - 2

Step-by-step explanation:

to calculate a term in the sequence subtract 5 from the previous term

give first term a₁  = 13 , then

a₂ = a₁ - 5 = 13 - 5 = 8

a₃ = a₂ - 5 = 8 - 5 = 3

a₄ = a₃ - 5 = 3 - 5 = - 2

On solving the provided question, we can say that since it it is right angled triangle so the relation that be formed is  [tex]m^2 = p^2 + z^2[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

since it it is right angled triangle

so the relation that be formed is

[tex]m^2 = p^2 + z^2[/tex]

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

In any function y = f(x) , set of all possible values of x define the domain of f(x), in the graph The curve in terms of x-axis(in 1st & 3rd quadrant) goes from -4 to -2(doesnt include -2).

So domain = [-4, -2)

Similarly, in 2nd and 4th quadrant, for x-axis

It goes from 2 to 5 (doesnt include 2 & 5)

So domain = (2, 5)

Hence,

Domain of the f(x) is [-4, -2) U (2, 5).

Range tells the possible values of y, for this function it goes from -5 to +3(doesnt include 3).

Range is [-5, 3)

Answer:

m = 2

Step-by-step explanation:

Slope = rise / run or (y2 - y1) / ( x2 - x1)

Let's pick 2 points (0,0) (1,2)

We see the y increase by 2 and the x increase by 1, so the slope is

m = 2

Answer:

15. -3 1/4

16. -4 1/2 OR -4 2/4

17. 1 1/4

18. -5 3/4

19. 1/2 OR 2/4

20. -2 1/2 OR -2 2/4

Step-by-step explanation:

Answer:

15) -3.25

16) -4.5

17)1.25

18)-5.75

19).5

20)-2.5

If the equation that relates the Runner 2’s distance (in miles) with time (in minutes) is [tex]t=8.5d[/tex]  then the slope/rate of change of Runner 2 is 8.5 minutes for 1 mile  .

The three runners are training for the marathon ,

The equation that relates the Runner 2’s distance (in miles) with time (in minutes) is ⇒ [tex]t=8.5d[/tex] ,

to cover the distance of 2 miles Runner2 will take [tex]t= 8.5 \times 2[/tex] minutes ;

So , [tex]t=17[/tex] minutes ;

the first point will be (2,17) .

and to cover the distance of 4 miles the runner 2 will take [tex]t= 8.5 \times 4[/tex]

So , [tex]t=34[/tex] minutes ;

the second point will be (4,34) .

we have to find the rate of change/slope of runner 2  ,

that can be written as : [tex]Slope = \frac{34-17}{4-2}[/tex]

On simplifying ,

we get ;

[tex]Slope = \frac{17}{2}[/tex] ;

So , [tex]Slope = 8.5[/tex].

Therefore , the rate of change of Runner 2 is 8.5 .

The given question is incomplete , the complete question is

Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. The equation that relates the Runner 2’s distance (in miles) with time (in minutes) is "t = 8.5d". Find the slope/rate of change of Runner 2 ?

Learn more about Slope here

https://brainly.com/question/29083538

#SPJ4

The growth in x years for the gym will be represented as [tex]y = 840(1.25)^x[/tex].

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

City Fitness, a popular gym currently has 840 members. Based on its membership statistics since opening a few years ago, City Fitness expects to grow its membership by a factor of 1/4.

The expression can be written as,

[tex]y = 840(1.25)^x[/tex].

To know more about an expression follow

https://brainly.com/question/11737323

#SPJ1

Answer:

There were 65 stars on his cape.

Step-by-step explanation:

So, there are 87 neon stars in total, and we are using 1 star for his wand, so there are 86 stars left on his cape and hat. We'll label the hat as h.

The stars are 2 more then 3 times the stars on his cape, plus the stars on his hat, so the equation is:

4h+2=86

4h=84

h=21

21x3+2=65

Answer:

There were 65 stars on his cape.

Step-by-step explanation:

So, there are 87 neon stars in total, and we are using 1 star for his wand, so there are 86 stars left on his cape and hat. We'll label the hat as h.

The stars are 2 more then 3 times the stars on his cape, plus the stars on his hat, so the equation is:

4h+2=86

4h=84

h=21

21x3+2=65

Answer:

15 mm have 1.5 cm.

Step-by-step explanation:

1 mm = 0.1 cm

1 cm = 10 mm

5 cm have 50 mm

and

15 mm have 1.5 cm.

Answer:

  135.5 m

Step-by-step explanation:

Given a triangle with angles A=46°, B=103°, and side c=97 m, you want to find the length of side 'a'.

Given one side and two angles we can solve the triangle using the Law of Sines:

  a/sin(A) = b/sin(B) = c/sin(C)

In order to do that, we need to have a (side, angle) pair, so we need to find the measure of angle C.

  A + B + C = 180°

  46° +103° +C = 180° . . . use the given measures

  C = 31° . . . . . . . . . . . . . subtract 149°

Now, we can find 'a' from ...

  a/sin(A) = c/sin(C)

  a = c·sin(A)/sin(C) = (97 m)·sin(46°)/sin(31°) ≈ 135.477286 m

The distance from B to the tree at C is about 135.5 meters.

Answer:

81 personas

Step-by-step explanation:

Lucía les cuenta una historia a 3 amigos a la hora 12.

Cada uno de ellos se comunica a 3 personas en los próximos 10 minutos.

a) Primeros 10 minutos

1 amigo = 3 personas = 10 minutos

3 amigos = x

Multiplicar cruzada

x = 3 × 3 personas = 9 personas

Por lo tanto, 9 personas han escuchado la historia en 10 minutos.

Si este trámite continúa, ¿cuántas personas han escuchado la noticia hasta las 12:30?

12: 30 - 12:00 = 30 minutos más

10

Por eso,

b) Segundos 10 minutos = 20 minutos

9 personas cada uno le dice a 3 personas en otros 10 minutos

1 persona = 3 personas

9 personas = x

Multiplicar cruzada

x = 9 × 3 personas

x = 27 personas

c) Los últimos 10 minutos = 30 minutos

1 persona = 3 personas

27 personas = x

Multiplicar cruzada

x = 27 × 3 personas

x = 81 personas

Por lo tanto, a los 30 minutos, 81 personas habrían escuchado la noticia a las 12:30

√6/3 is the value after rationalization of √2/√3

An expression is combination of variables, numbers and operators.

The given expression is √2/√3

Square root two divided by square root three.

We need to rationalize the denominator

To rationalize multiply numerator and denominator by √3

√2/√3×√3/√3

√2×3/3

√6/3

Hence, √6/3 is the value after rationalization of √2/√3

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ1

Answer:

Step-by-step explanation:

The area formula of a parallelogram is the same as the area formula of a rectangle, it is A=bh.

Given that area is 15 units, A = 15.

On the graph, we can see that base is 3 units. b = 3.

plug in the values into the formula,

[tex]15 = 3 * h\\h = 15 / 3 = 5[/tex]

Answer:

I took the Quiz and got 19,958,400 ways wrong from the previous answer the real answer is 496 ways

Step-by-step explanation:

The number of different ways that you can put 8 books on the shelf will be 495.

A permutation is an act of arranging items or elements in the correct order. Combinations are a way of selecting items or pieces from a group of objects or sets when the order of the components is immaterial.

Then the combination is given as,

⇒ ⁿCₐ

Where n is total sample and a is the selected sample from n.

You have 12 books, and you want to put 8 on a shelf in your room.

Order does not matter to you.

Then the number of different ways that you can put 8 books on the shelf will be

⇒ ¹²C₈

⇒ 12! / [(12 – 8)! x 8!]

⇒ 12 x 11 x 10 x 9 x 8! / (4 x 3 x 2 x 1 x 8!)

⇒ 11 x 5 x 9

⇒ 495

Thus, the number of different ways that you can put 8 books on the shelf will be 495.

More about the permutation and the combination link is given below.

https://brainly.com/question/11732255

#SPJ5

Answer:

down there with the work :)

Step-by-step explanation:

formula: a^2+b^2=c^2

Page 1:

1)

6^2+8^2=c^2

36+64=c^2

100=c^2

take the square root of both sides

c=10

2)

8^2+b^2=12^2

64+b^2=144

80=b^2

b=[tex]4\sqrt{5}[/tex]

3)

14^2+b^2=48^2

196+b^2=2304

b^2=2108

b=[tex]2\sqrt{527}[/tex]

Page 2:

1)

5^2+11^2=13^2

25+121=169

no this is not true so this is not a right triangle

2)

10^2+24^2=26^2

100+576=676

this is true so this IS a right triangle

hope this helps!

Answer:

80/89 (I messed it up with sine sorry :)

Answer:

cos ∅ = 80/89

Step-by-step explanation:

As required from the question the picture below represent a triangle UVW . The angle W = 90°. The sides WV = 39 , VU = 89 and UW = 80. The triangle forms a right angle triangle .

Such triangle one can establish trigonometric relationship using the SOHCAHTOA principle.

The question requested us to find the ratio that represent the cosine of  ∠U.

The ∠U is represented as ∅ .

Therefore,

cos ∅ = adjacent/hypotenuse

adjacent = 80. The adjacent side is the non hypotenuse side that is next to the given angle.

hypotenuse = 89 . Hypotenuse is the longest side of a right angle triangle and it opposite the right angle.  

cos ∅ = adjacent/hypotenuse

cos ∅ = 80/89

Answer:

No

Step-by-step explanation:

4 5/8 = 4.625 because 458=4+(5÷8)=4+0.625=4.625

4.65>4.625 so she has less

A total of 3 five ounces glass are needed so have the same alcohol as that of a 12 ounce glass.

In order to find the number of glass of capacity five ounces that will have the same capacity as that of the twelve ounce glass can be calculated as followed,

Let us say that n number of five ounces glasses are required to equate 12 ounce glass.

Now, we can write the relation,

using simple algebra,

n(Five ounces glasses) = 1 Ounce alcohol content

n = 12/5

n = 2.4

But, we have to answer an integral value, so, we will say that the required number of the glasses is 3.

To know more about algebra, visit,

https://brainly.com/question/4344214

#SPJ4

When reflected in the y-axis, the image of the point (2/3) is (-2/3).

The sign of the x coordinate changes when a point is mirrored on the y-axis.

When a figure is built around a single point known as the point of reflection or the figure's centre, a reflection point results. There is an exact opposite point on the other side of each point in the figure. The shape and dimensions of the figure remain unchanged underneath the point of reflection.

The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).

For more questions on reflection of point

https://brainly.com/question/26642069

#SPJ4

Answer: x = a/b - c

Step-by-step explanation:

First divide by b on each side to get the x by itself.

Then subtract c from both sides to make x the subject of the formula.

Step-by-step explanation:

a = bx + c

the goal is to get to a form with "x = ...".

a - c = bx

(a - c)/b = x

done.

Answer:

170.52 in

Step-by-step explanation:

The first ferry's speed is 18.5 mph and the second ferry, which is slower, travels at 13.5 mph.

Let x represent the first ferry's speed.

The second, slower ferry's speed is then x-5 (since 5 miles per hour slower)

First ferry time equals distance/speed equals

50/x

Time spent on the second ferry:

50 / x - 5

The difference in times is 1 hour because the second ferry departs an hour earlier.

50 / x - 5 - 50/x = 1

50x - 50(x - 5) = x (x - 5 )

250 = x² - 5x

x² - 5x - 250 = 0

(x - 10 )(x + 5) = 0

x = 18.5 - 13.5

Speed can never be detrimental.

Therefore, the first ferry's speed is 18.5 mph.

and the second ferry, which is slower, travels at 13.5 mph.

To Learn more About ferry's speed Refer To:

https://brainly.com/question/28757057

#SPJ4

The largest side of the length is 26cm.

Now, According to the question:

Three consecutive even numbers can be expressed in terms of n. If n is an even number then,

(n -2), (n), (n + 2)

are three consecutive even numbers.

Therefore,

(n -2)+ (n)+ (n + 2) = 72cm.

We can simplify so...

3n + 2 - 2 = 72 cm.

3n + 0 = 72 cm.

3n = 72cm.

Divide both sides by 3 to solve for n

n = 24 cm.

24 is an even integer. Input 24 into the original equation.

(n -2)+ (n)+ (n + 2) = 72cm.

(24 - 2) + 24 + (24 + 2) = 72cm

22 + 24 + 26 = 72

72 = 72

Hence, The largest side of the length is 26cm.

Learn more about Triangle at:

https://brainly.com/question/18244236

#SPJ4

To ride a bike to school Torrin takes 15.75 min to ride to school and 3.54 km is the distance from his house to school.

Let  v₁ = 13.5 km/h the speed to school

v₂ = 10.5 km the speed returning home

t = the time of the ride to school in minutes

36 - t = the time of the ride from school in minutes

Since, distance = speed × time

⇒v₁ × t/60 = v₂ × (36 - t)/60

⇒13.5 × t/60 = 10.5 × (36 - t)/60

⇒t = 15.75 min

Now, the distance = v₁ × t/60 = 13.5 × 15.75/60 = 3.54 km.

To know more about distance, here

https://brainly.com/question/15172156

#SPJ4